Transum Software

Exam-Style Questions.

Problems adapted from questions set for previous Mathematics exams.

1.

GCSE Higher

Without using a calculator, show clearly that \(27^{\frac23}\) is equal to \(9\).


2.

GCSE Higher

There's an old Elvish wives tale that roughly translated reads:

Four To The Half Power Is Simple To Do

Just Halve The Four And The Answer Is Two.

Modern-day Elves extend this method to calculate other powers such as

$$ 16^{ \frac{1}{4}} = \frac{1}{4} \text{ of } 16 = 4 $$

Is this calculation correct? If it is not explain what is wrong.


3.

GCSE Higher
$$ 9^{\frac{1}{3}} \times 3^n = 27^{\frac{4}{5}} $$

Work out the exact value of \(n\).


4.

GCSE Higher

Without using a calculator find the values of the following:

(a) \(25^{-\frac12} \)

(b) \( \left( \frac{27}{64} \right)^{ \frac23} \)


5.

GCSE Higher

If a, b and c are positive integers use the following statements to find the values of a, b and c.

$$ (ab^c)^3 = 27b^{21} $$ $$ b= 9a $$

6.

GCSE Higher

\(y = a \times b^{x – 2}\) where \(a\) and \(b\) are numbers.

\(y = 5\) when \(x = 2\)

\(y = 0.005\) when \(x = 5\)

Work out the value of \(y\) when \(x = 4\)


If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

 

Exam-Style Questions Main Page

 

Search for exam-style questions containing a particular word or phrase:

To search the entire Transum website use the search box in the grey area below.

Comments:

Apple

©1997-2024 WWW.TRANSUM.ORG